{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introduction to Quantitative Finance\n",
    "\n",
    "Copyright (c) 2019 Python Charmers Pty Ltd, Australia, <https://pythoncharmers.com>. All rights reserved.\n",
    "\n",
    "<img src=\"img/python_charmers_logo.png\" width=\"300\" alt=\"Python Charmers Logo\">\n",
    "\n",
    "Published under the Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) license. See `LICENSE.md` for details.\n",
    "\n",
    "Sponsored by Tibra Global Services, <https://tibra.com>\n",
    "\n",
    "<img src=\"img/tibra_logo.png\" width=\"300\" alt=\"Tibra Logo\">\n",
    "\n",
    "\n",
    "## Module 2.2: Modelling Techniques\n",
    "\n",
    "### 2.2.3 ARCH and GARCH\n",
    "\n",
    "Put simply, the ARCH model is the AR model, applied to the variance in residuals of a previously trained model. The GARCH model is the same analysis of the residuals a model, except using the ARMA model. Before we look further, we first outline some of the key attributes that GARCH deals with.\n",
    "\n",
    "**Heteroskedasticity** refers to the attribute of some variables to have a variance of residuals that varies wildly (almost everyone uses the term \"wildly\" here, therefore it is basically official terminology). It is indicative that there may be more factors that explain the way in which the data varies. *Homoskedastic* variables have a consistent variance, a key component, but not a sufficient one for stationarity (for instance, the variance may be constant, but there may be a trend in the mean).\n",
    "\n",
    "A **conditional heteroskedastic** variable is one that has a conditional component. For instance, if the market drops, it might go into panic, causing further drops. This drop was conditional on the previous drop.\n",
    "\n",
    "We now have the necessary components to understand the ARCH and GARCH models:\n",
    "\n",
    "* ARCH stands for Autoregressive Conditionally Heteroskedastic\n",
    "* GARCH stands for Generalized Autoregressive Conditionally Heteroskedastic \n",
    "\n",
    "We apply ARCH and GARCH models *after* we have fitted a model to the original dataset. Importantly, the residuals after fitting that first model should look like it is discrete noise. The ARCH modelling then looks for a pattern in the residuals of that model, specifically at a given lag. It is this variance over time that autoregressive models cannot model, and where the ARCH and GARCH models help.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ARCH Models\n",
    "\n",
    "The ARCH(1) model is given by:\n",
    "\n",
    "$ Var(y_t) = \\alpha_0 + \\alpha_1 y_{t-1}^2$\n",
    "\n",
    "\n",
    "Which is the AR model, but on variance instead of raw values.\n",
    "\n",
    "The GARCH(1,1) model is \n",
    "\n",
    "$Var(y_t) = \\alpha_0 + \\alpha_1 y_{t-1}^2  + \\alpha_2 Var(y_{t-1})$\n",
    "\n",
    "Which you'll notice is the ARMA model applied to the variance rather than the absolute value. The model is stable only if the sum of all $\\alpha_i$ values is less than 1. \n",
    "\n",
    "Generalisations, such as GARCH(2, 2) are also possible by adding further lagged terms to each of the AR and MA components of the equation, in the same manner they can, for instance, be added to ARIMA.\n",
    "\n",
    "We'll generate some data that fits this model, and then shown the residual graph and autocorrelations, highlighting what a dataset that fits ARCH/GARCH looks like."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%run setup.ipy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = np.zeros(1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "y[0] = np.random.normal()\n",
    "for i in range(1, len(y)):\n",
    "    y[i] = np.random.normal() * np.sqrt(5 + 0.75 * y[i-1]**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x23cdb582510>]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "from statsmodels.graphics.tsaplots import plot_acf, plot_pacf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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YDgEHAACYDgEHAACYDgEHAACYDgEHAACYDgEHAACYDgEHAACYDgEHAACYDgEHAACYDgEHAACYDgEHAACYDgEHAACYDgEHAACYDgEHAACYDgEHAACYDgEHAACYDgEHAACYDgEHAACYDgEHAACYDgEHAACYDgEHAACYDgEHAACYDgEHAACYDgEHAACYDgEHAACYDgEHAACYDgEHAACYDgEHAACYDgEHAACYDgEHAACYDgEHAACYTosEnGXLlqlHjx7y8fFRbGystm/fXmPZkSNHymKxVBluvPFGR5lJkyZVmZ6UlNQSXQEAAG1AB1cvYN26dUpJSdHy5csVGxurJUuWKDExUbm5uQoJCalS/vXXX1dZWZnj9alTpzRw4EDdeeedTuWSkpK0cuVKx2ur1eq6TgAAgDbF5UdwFi9erOTkZE2ePFnR0dFavny5fH19tWLFimrLd+nSRWFhYY4hIyNDvr6+VQKO1Wp1KhcYGOjqrgAAgDbCpQGnrKxMOTk5SkhI+GGBHh5KSEhQdnZ2vep4+eWXNX78eHXq1MlpfFZWlkJCQtSnTx9NmzZNp06dqrGO0tJS2e12pwEAAJiXSwPOyZMnVV5ertDQUKfxoaGhstlsdc6/fft2ffXVV/r1r3/tND4pKUmvvPKKMjMz9dRTT2nr1q0aPXq0ysvLq60nLS1N/v7+jiEyMrLxnQIAAK2ey6/BaYqXX35Z/fv315AhQ5zGjx8/3vH//v37a8CAAerVq5eysrIUHx9fpZ7U1FSlpKQ4XtvtdkIOAAAm5tIjOEFBQfL09FRBQYHT+IKCAoWFhdU6b3FxsdauXaspU6bUuZyoqCgFBQVp//791U63Wq3y8/NzGgAAgHm5NOB4e3srJiZGmZmZjnEVFRXKzMxUXFxcrfOuX79epaWluvvuu+tczpEjR3Tq1CmFh4c3uc0AAKDtc/ldVCkpKXrppZe0evVq7dmzR9OmTVNxcbEmT54sSZo4caJSU1OrzPfyyy9rzJgx6tq1q9P4s2fP6uGHH9ann36qgwcPKjMzU7feeqt69+6txMREV3cHAAC0AS6/BmfcuHE6ceKE5s2bJ5vNpkGDBik9Pd1x4fGhQ4fk4eGcs3Jzc/XRRx9p06ZNVerz9PTU7t27tXr1ahUWFioiIkKjRo3SokWLeBYOAACQJFkMwzDc3YiWZrfb5e/vr6Kioma9Hqek7KKi570vSfpmYaJ8vVv1NdwAALQpDdl/81tUAADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdFok4Cxbtkw9evSQj4+PYmNjtX379hrLrlq1ShaLxWnw8fFxKmMYhubNm6fw8HB17NhRCQkJ2rdvn6u7AQAA2giXB5x169YpJSVF8+fP186dOzVw4EAlJibq+PHjNc7j5+en/Px8x/Dtt986TX/66ae1dOlSLV++XNu2bVOnTp2UmJio8+fPu7o7AACgDXB5wFm8eLGSk5M1efJkRUdHa/ny5fL19dWKFStqnMdisSgsLMwxhIaGOqYZhqElS5bo0Ucf1a233qoBAwbolVde0bFjx/TGG2+4ujsAAKANcGnAKSsrU05OjhISEn5YoIeHEhISlJ2dXeN8Z8+eVffu3RUZGalbb71VX3/9tWNaXl6ebDabU53+/v6KjY2tsc7S0lLZ7XanAQAAmJdLA87JkydVXl7udARGkkJDQ2Wz2aqdp0+fPlqxYoXefPNN/e1vf1NFRYWGDh2qI0eOSJJjvobUmZaWJn9/f8cQGRnZ1K4BAIBWrNXdRRUXF6eJEydq0KBBGjFihF5//XUFBwfrxRdfbHSdqampKioqcgyHDx9uxhYDAIDWxqUBJygoSJ6eniooKHAaX1BQoLCwsHrV4eXlpSuvvFL79++XJMd8DanTarXKz8/PaQAAAObl0oDj7e2tmJgYZWZmOsZVVFQoMzNTcXFx9aqjvLxcX375pcLDwyVJPXv2VFhYmFOddrtd27Ztq3edAADA3Dq4egEpKSm65557NHjwYA0ZMkRLlixRcXGxJk+eLEmaOHGiLr30UqWlpUmSFi5cqKuvvlq9e/dWYWGhnnnmGX377bf69a9/Len7O6xmzpypJ554Qpdffrl69uypxx57TBERERozZoyruwMAANoAlweccePG6cSJE5o3b55sNpsGDRqk9PR0x0XChw4dkofHDweSvvvuOyUnJ8tmsykwMFAxMTH65JNPFB0d7SjzyCOPqLi4WFOnTlVhYaGGDRum9PT0Kg8EBAAA7ZPFMAzD3Y1oaXa7Xf7+/ioqKmrW63FKyi4qet77kqRvFibK19vl+REAgHajIfvvVncXFQAAQFMRcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOm0SMBZtmyZevToIR8fH8XGxmr79u01ln3ppZd07bXXKjAwUIGBgUpISKhSftKkSbJYLE5DUlKSq7sBAADaCJcHnHXr1iklJUXz58/Xzp07NXDgQCUmJur48ePVls/KytJdd92lLVu2KDs7W5GRkRo1apSOHj3qVC4pKUn5+fmO4e9//7uruwIAANoIlwecxYsXKzk5WZMnT1Z0dLSWL18uX19frVixotrya9as0f33369Bgwapb9+++utf/6qKigplZmY6lbNarQoLC3MMgYGBru4KAABoI1wacMrKypSTk6OEhIQfFujhoYSEBGVnZ9erjpKSEl24cEFdunRxGp+VlaWQkBD16dNH06ZN06lTp2qso7S0VHa73WkAAADm5dKAc/LkSZWXlys0NNRpfGhoqGw2W73qmDNnjiIiIpxCUlJSkl555RVlZmbqqaee0tatWzV69GiVl5dXW0daWpr8/f0dQ2RkZOM7BQAAWr0O7m5AbZ588kmtXbtWWVlZ8vHxcYwfP3684//9+/fXgAED1KtXL2VlZSk+Pr5KPampqUpJSXG8ttvthBwAAEzMpUdwgoKC5OnpqYKCAqfxBQUFCgsLq3XeZ599Vk8++aQ2bdqkAQMG1Fo2KipKQUFB2r9/f7XTrVar/Pz8nAYAAGBeLg043t7eiomJcbpAuPKC4bi4uBrne/rpp7Vo0SKlp6dr8ODBdS7nyJEjOnXqlMLDw5ul3QAAoG1z+V1UKSkpeumll7R69Wrt2bNH06ZNU3FxsSZPnixJmjhxolJTUx3ln3rqKT322GNasWKFevToIZvNJpvNprNnz0qSzp49q4cffliffvqpDh48qMzMTN16663q3bu3EhMTXd0dAADQBrj8Gpxx48bpxIkTmjdvnmw2mwYNGqT09HTHhceHDh2Sh8cPOevPf/6zysrKdMcddzjVM3/+fD3++OPy9PTU7t27tXr1ahUWFioiIkKjRo3SokWLZLVaXd0dAADQBlgMwzDc3YiWZrfb5e/vr6Kioma9Hqek7KKi570vSfpmYaJ8vVv1NdwAALQpDdl/81tUAADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdAg4AADAdDq4uwFwD8MwWnh5Lbo4U2HV1U9Lb9NVll/X9EY2z2jBLYDPadvQFt6nDp4WeXm69xgKAaeF7Th4WuUVrt8628IHAABgThEBPuretZNb20DAaWEVFQbhA2jH8ovOKSv3hE6cLVVwZ6tG9glWuH9HdzcLMB0CDgC0kKzc4/rLv/4ji74/pWWR9NbuY7p3eJRG/CTEza2DuxB6XYOAAwAtIL/onP7yr//IMH64Xqfy3xc//I/6hPopzN/HXc1rddrLTp/Q6zoEHKAVai9f7u1JVu4Jx07sv1kkbck9rruGdGvhVrVO7WWnT+h1LQIO4EKNCSrt5cu9vTlxtrTG+6GM/z+9Lu0h+LannT6h17UIOGhx7eFLWmpcUGlPX+4/5o5toqWXGdzZWuvOLLiztdb522LwbVzAb9pO313fL41ZbnOEXndoK9/hBJx2zB0bqbu+pFu6r40NKu3xLzp3bBPuWObIPsF6a/exaqcZkq7rU/Ny3Rl8G/vZaew6bspO313fL41dblNDrzu0paDdIk/hWbZsmXr06CEfHx/FxsZq+/bttZZfv369+vbtKx8fH/Xv31/vvvuu03TDMDRv3jyFh4erY8eOSkhI0L59+1zZBdPJyj2u2eu/0Nu7j+nT/5zS27uPafb6L7T138ddtswff0lXGHL698UP/yNb0XmXLNcdfa0MKtWpDCrVaat/0TWWO7YJd22H4f4dde/wKFl+tGF4WCSLRbp3eFStAaWx21NTNfaz05R1XLnTr05tO313va9NWe7IPsG1ft5rC73u4K513FguP4Kzbt06paSkaPny5YqNjdWSJUuUmJio3NxchYRUffM++eQT3XXXXUpLS9NNN92kV199VWPGjNHOnTt1xRVXSJKefvppLV26VKtXr1bPnj312GOPKTExUd988418fOr/V0xJ2UV1KLvYbH0t+VFdJTXUe/5CuVrgOX+1stnP1/rXYI+unRTq1/x/DX6wp6DWv1Yy9th0Z0xksy7TXX0tsJ+v9YurwH5e5y+UV5kW6OtV6zoK9PWqdr4fs9nP61/7TujU2TJ17eytay8PVpgL+tgc3LFNuGOZlWJ7dlWEv4/mbfxGkvTzfqG6rm+IQv18an1fG7s9NUVTPjtNWcdxvbrWeqRraK+u1fbVXe9rU5Yb6OutXw3tqRUf5znm97B8X9evhvZUgAs/742ZryF9PVdWXuN+sCkaUqfFcPHzzWNjY3XVVVfp+eeflyRVVFQoMjJSDzzwgObOnVul/Lhx41RcXKy3337bMe7qq6/WoEGDtHz5chmGoYiICM2ePVsPPfSQJKmoqEihoaFatWqVxo8fX6XO0tJSlZb+8Jev3W5XZGSkImf+Qx5W3+buMgAAcIGK0hIdXvILFRUVyc/Pr9ayLj1FVVZWppycHCUkJPywQA8PJSQkKDs7u9p5srOzncpLUmJioqN8Xl6ebDabUxl/f3/FxsbWWGdaWpr8/f0dQ2Ska/46AwAArYNLT1GdPHlS5eXlCg0NdRofGhqqvXv3VjuPzWartrzNZnNMrxxXU5n/lpqaqpSUFMfryiM4238XX2cCbG478k47naL6174TWvnxwWoPTw67PKjO+kovlOu+NTslScsn/ExWL88651mfc1jpX9mqPVXmYZGSrgir81BuY5Zrs5/Xbzd8We1PVVgsUtpt/as95N3Y+ST39VWSPtp3Uis+yXO6GK++722B/bw+/NHh4+GXB9d5Kq05+nroVLHmv/X96ZPE6FCN7BtS52Hrprw/TZlXatntsKnLbaqmbE8t/T3RHOu4odz1vrqjr1Lj35+Wel/D/X3UrWvznyGx2+0KX1K/su3iLiqr1SqrteqFab7eHeTr3bKrwMfL07Fh5Red08pPDjqdz6yctuKTPF1xqX+D7oywennKpx4fyIR+oXrvq+rDoCHp5/3C6qzHZv/hYrKNu48poV9onXdW9OjaSfcOj9KLH/6nypf0vcOjavxhtuwDp2o97/vJgVM13lnkrr5KUkJ0qK641F9bco877kC5rk9Ivd7T7l076X8a+EN135VcqPU6je9KLtTa18q7Iypl7CnQpj0Fdd4d0ZT3p7HbRKWW3A5rUt/PXVM1ZXv6sZb4nmjudVwfzbHM1rA91VdjP+9N+Z5oSF87enu6ZP96sQF1unTvHhQUJE9PTxUUFDiNLygoUFhYWLXzhIWF1Vq+8t+CggKFh4c7lRk0aFAztt713HVLcOXdHDVtpHV9Yf73jjD9K5ve+8pWr9sER/wkRH1C/Rr0Jd2UO4vc2VdJCvP3abHbuptyy+mP746oVBm267oNual3fjVmm5BafjtsDRq7Pf14x70+53C9dtxN/ey4Yx03ZZltbXtq7Oe9qbemt6XPjksDjre3t2JiYpSZmakxY8ZI+v4i48zMTM2YMaPaeeLi4pSZmamZM2c6xmVkZCguLk6S1LNnT4WFhSkzM9MRaOx2u7Zt26Zp06a5sjvNzp23BDd2I23KjrBSQ7+k3fWBbI6+tqSmPGelKWG7OZ7l0dBtwh3bYVvlzh23O9ZxY5bZFrenxn7em/I9UamtfHZc/hyclJQUvfTSS1q9erX27NmjadOmqbi4WJMnT5YkTZw4UampqY7yv/nNb5Senq7//d//1d69e/X444/rs88+cwQii8WimTNn6oknntDGjRv15ZdfauLEiYqIiHCEqLaisc97aC6VG+mD11+uu4Z0q+dfOS3/PI7meFZEW+lrU/z4OSuVz1ep73NWmhK23fEsj7b23rhLTTvuhjy3pDGfnbamLW5Pjf28N+V7oq1x+QUo48aN04kTJzRv3jzZbDYNGjRI6enpjouEDx06JA+PH3LW0KFD9eqrr+rRRx/Vb3/7W11++eV64403HM/AkaRHHnlExcXFmjp1qgoLCzVs2DClp6c36Bk4rUFzJOnGHHpuCnccdWrqofLGaosP3WvsX9xNOQrjjvfH3e9NS3/uGqs9Phm7Mdy9PTVWYz/vbek0U1O4/Dk4rZHdbpe/v3+97qNvbtv+c8rp6vWt/z5e446hrsPHlYeeK9/ByjuwXPnI7L9vP6S3dx+r8Qr8mwZEuOwL01Z0vkU/kO7sa0vLLzqn2eu/qPHuiMV3DqpzXbfk++PO98Ydn7vGWrp5nz79z6ka39ero7rqwesvb/mGtTLt6bPeUiICfFxygXVD9t/t4i6q1qytXR/SHEedGqutnONui5rjKExLvj/uem/a2nVZbfG3jtyhPX3W25MW+S0q1K4tXR/Sns7ftqe+St+H7cV3DtJNAyJ0dVRX3TQgQovvHNTqjkpI7ntv2tq1Gm3tt47cpb191tsLjuC0UW3xDqy2qD31VWo7d0dI7nlv2tq1Gu66fq0tam+f9faAgNPCOnh6qKIZLnsK9av90HPoJVZ5etT0t+b3v8jeFBEBPpoQW/8dYVu+0Cs8wEe/bEBfm1v7u0qu/lo6kLXFUz7suOuvLQV81I2A08Jiugc2Sz1Bna3auKv6c8aSNDPhJ+oR5JonaAKu0trveQj1s+rtGq7VkKSZCZerRy0XVjamd821Tm4eGF53oR8vt1mWai6tefM0Wtk75mmp+Q/slkLAaaN6BnXSU2MHaM4/d8tiscgwDMe/T40dQLhBm2RpBV+KtYkK7lzr5y4quLMLltq61wnQWnGbeAvfJt7cDp4s1rrPDuvId+d0WWBHjRscSbgBXIzPHeAeDdl/E3DaeMABAKC9aMj+m9vEAQCA6RBwAACA6RBwAACA6RBwAACA6RBwAACA6RBwAACA6RBwAACA6RBwAACA6RBwAACA6RBwAACA6RBwAACA6RBwAACA6RBwAACA6RBwAACA6RBwAACA6RBwAACA6RBwAACA6RBwAACA6RBwAACA6RBwAACA6RBwAACA6RBwAACA6RBwAACA6RBwAACA6RBwAACA6RBwAACA6RBwAACA6bg04Jw+fVoTJkyQn5+fAgICNGXKFJ09e7bW8g888ID69Omjjh07qlu3bnrwwQdVVFTkVM5isVQZ1q5d68quAACANqSDKyufMGGC8vPzlZGRoQsXLmjy5MmaOnWqXn311WrLHzt2TMeOHdOzzz6r6Ohoffvtt7rvvvt07Ngxvfbaa05lV65cqaSkJMfrgIAAV3YFAAC0IRbDMAxXVLxnzx5FR0drx44dGjx4sCQpPT1dN9xwg44cOaKIiIh61bN+/XrdfffdKi4uVocO3+cxi8WiDRs2aMyYMY1qm91ul7+/v4qKiuTn59eoOgAAQMtqyP7bZaeosrOzFRAQ4Ag3kpSQkCAPDw9t27at3vVUdqIy3FSaPn26goKCNGTIEK1YsUK15bTS0lLZ7XanAQAAmJfLTlHZbDaFhIQ4L6xDB3Xp0kU2m61edZw8eVKLFi3S1KlTncYvXLhQ119/vXx9fbVp0ybdf//9Onv2rB588MFq60lLS9OCBQsa1xEAANDmNPgIzty5c6u9yPfHw969e5vcMLvdrhtvvFHR0dF6/PHHnaY99thjuuaaa3TllVdqzpw5euSRR/TMM8/UWFdqaqqKioocw+HDh5vcPgAA0Ho1+AjO7NmzNWnSpFrLREVFKSwsTMePH3caf/HiRZ0+fVphYWG1zn/mzBklJSXpkksu0YYNG+Tl5VVr+djYWC1atEilpaWyWq1Vplut1mrHAwAAc2pwwAkODlZwcHCd5eLi4lRYWKicnBzFxMRIkjZv3qyKigrFxsbWOJ/dbldiYqKsVqs2btwoHx+fOpe1a9cuBQYGEmIAAIAkF16D069fPyUlJSk5OVnLly/XhQsXNGPGDI0fP95xB9XRo0cVHx+vV155RUOGDJHdbteoUaNUUlKiv/3tb04XBAcHB8vT01NvvfWWCgoKdPXVV8vHx0cZGRn6wx/+oIceeshVXQEAAG2MS5+Ds2bNGs2YMUPx8fHy8PDQ2LFjtXTpUsf0CxcuKDc3VyUlJZKknTt3Ou6w6t27t1NdeXl56tGjh7y8vLRs2TLNmjVLhmGod+/eWrx4sZKTk13ZFQAA0Ia47Dk4rRnPwQEAoO1pFc/BAQAAcBcCDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB2XBpzTp09rwoQJ8vPzU0BAgKZMmaKzZ8/WOs/IkSNlsVichvvuu8+pzKFDh3TjjTfK19dXISEhevjhh3Xx4kVXdgUAALQhHVxZ+YQJE5Sfn6+MjAxduHBBkydP1tSpU/Xqq6/WOl9ycrIWLlzoeO3r6+v4f3l5uW688UaFhYXpk08+UX5+viZOnCgvLy/94Q9/cFlfAABA22ExDMNwRcV79uxRdHS0duzYocGDB0uS0tPTdcMNN+jIkSOKiIiodr6RI0dq0KBBWrJkSbXT33vvPd100006duyYQkNDJUnLly/XnDlzdOLECXl7e9fZNrvdLn9/fxUVFcnPz69xHQQAAC2qIftvl52iys7OVkBAgCPcSFJCQoI8PDy0bdu2Wudds2aNgoKCdMUVVyg1NVUlJSVO9fbv398RbiQpMTFRdrtdX3/9dbX1lZaWym63Ow0AAMC8XHaKymazKSQkxHlhHTqoS5custlsNc73y1/+Ut27d1dERIR2796tOXPmKDc3V6+//rqj3h+HG0mO1zXVm5aWpgULFjSlOwAAoA1pcMCZO3eunnrqqVrL7Nmzp9ENmjp1quP//fv3V3h4uOLj43XgwAH16tWrUXWmpqYqJSXF8dputysyMrLRbQQAAK1bgwPO7NmzNWnSpFrLREVFKSwsTMePH3caf/HiRZ0+fVphYWH1Xl5sbKwkaf/+/erVq5fCwsK0fft2pzIFBQWSVGO9VqtVVqu13ssEAABtW4MDTnBwsIKDg+ssFxcXp8LCQuXk5CgmJkaStHnzZlVUVDhCS33s2rVLkhQeHu6o9/e//72OHz/uOAWWkZEhPz8/RUdHN7A3AADAjFx2kXG/fv2UlJSk5ORkbd++XR9//LFmzJih8ePHO+6gOnr0qPr27es4InPgwAEtWrRIOTk5OnjwoDZu3KiJEydq+PDhGjBggCRp1KhRio6O1v/8z//oiy++0Pvvv69HH31U06dP5ygNAACQ5OIH/a1Zs0Z9+/ZVfHy8brjhBg0bNkx/+ctfHNMvXLig3Nxcx11S3t7e+uCDDzRq1Cj17dtXs2fP1tixY/XWW2855vH09NTbb78tT09PxcXF6e6779bEiROdnpsDAADaN5c9B6c14zk4AAC0Pa3iOTgAAADuQsABAACmQ8ABAACmQ8ABAACmQ8ABAACmQ8ABAACmQ8ABAACmQ8ABAACmQ8ABAACmQ8ABAACmQ8ABAACmQ8ABAACmQ8ABAACmQ8ABAACmQ8ABAACmQ8ABAACmQ8ABAACmQ8ABAACmQ8ABAACmQ8ABAACmQ8ABAACmQ8ABAACmQ8ABAACmQ8ABAACmQ8ABAACmQ8ABAACmQ8ABAACmQ8ABAACmQ8ABAACmQ8ABAACmQ8ABAACmQ8ABAACmQ8ABAACmQ8ABAACmQ8ABAACm49KAc/r0aU2YMEF+fn4KCAjQlClTdPbs2RrLHzx4UBaLpdph/fr1jnLVTV+7dq0ruwIAANqQDq6sfMKECcrPz1dGRoYuXLigyZMna+rUqXr11VerLR8ZGan8/HyncX/5y1/0zDPPaPTo0U7jV65cqaSkJMfrgICAZm8/AABom1wWcPbs2aP09HTt2LFDgwcPliQ999xzuuGGG/Tss88qIiKiyjyenp4KCwtzGrdhwwb94he/UOfOnZ3GBwQEVCkLAAAgufAUVXZ2tgICAhzhRpISEhLk4eGhbdu21auOnJwc7dq1S1OmTKkybfr06QoKCtKQIUO0YsUKGYZRYz2lpaWy2+1OAwAAMC+XHcGx2WwKCQlxXliHDurSpYtsNlu96nj55ZfVr18/DR061Gn8woULdf3118vX11ebNm3S/fffr7Nnz+rBBx+stp60tDQtWLCgcR0BAABtToOP4MydO7fGC4Erh7179za5YefOndOrr75a7dGbxx57TNdcc42uvPJKzZkzR4888oieeeaZGutKTU1VUVGRYzh8+HCT2wcAAFqvBh/BmT17tiZNmlRrmaioKIWFhen48eNO4y9evKjTp0/X69qZ1157TSUlJZo4cWKdZWNjY7Vo0SKVlpbKarVWmW61WqsdDwAAzKnBASc4OFjBwcF1louLi1NhYaFycnIUExMjSdq8ebMqKioUGxtb5/wvv/yybrnllnota9euXQoMDCTEAAAASS68Bqdfv35KSkpScnKyli9frgsXLmjGjBkaP3684w6qo0ePKj4+Xq+88oqGDBnimHf//v368MMP9e6771ap96233lJBQYGuvvpq+fj4KCMjQ3/4wx/00EMPuaorAACgjXHpc3DWrFmjGTNmKD4+Xh4eHho7dqyWLl3qmH7hwgXl5uaqpKTEab4VK1bosssu06hRo6rU6eXlpWXLlmnWrFkyDEO9e/fW4sWLlZyc7MquAACANsRi1HZ/tUnZ7Xb5+/urqKhIfn5+7m4OAACoh4bsv/ktKgAAYDoEHAAAYDoEHAAAYDoEHAAAYDoEHAAAYDoEHAAAYDoEHAAAYDoEHAAAYDoEHAAAYDoEHAAAYDoEHAAAYDoEHAAAYDoEHAAAYDoEHAAAYDoEHAAAYDoEHAAAYDoEHAAAYDoEHAAAYDoEHAAAYDoEHAAAYDoEHAAAYDoEHAAAYDoEHAAAYDoEHAAAYDoEHAAAYDoEHAAAYDoEHAAAYDoEHAAAYDoEHAAAYDoEHAAAYDoEHAAAYDoEHAAAYDoEHAAAYDoEHAAAYDoEHAAAYDouCzi///3vNXToUPn6+iogIKBe8xiGoXnz5ik8PFwdO3ZUQkKC9u3b51Tm9OnTmjBhgvz8/BQQEKApU6bo7NmzLugBAABoq1wWcMrKynTnnXdq2rRp9Z7n6aef1tKlS7V8+XJt27ZNnTp1UmJios6fP+8oM2HCBH399dfKyMjQ22+/rQ8//FBTp051RRcAAEAbZTEMw3DlAlatWqWZM2eqsLCw1nKGYSgiIkKzZ8/WQw89JEkqKipSaGioVq1apfHjx2vPnj2Kjo7Wjh07NHjwYElSenq6brjhBh05ckQRERH1apPdbpe/v7+Kiork5+fXpP4BAICW0ZD9d4cWalOd8vLyZLPZlJCQ4Bjn7++v2NhYZWdna/z48crOzlZAQIAj3EhSQkKCPDw8tG3bNt12223V1l1aWqrS0lLH66KiIknfrygAANA2VO6363NsptUEHJvNJkkKDQ11Gh8aGuqYZrPZFBIS4jS9Q4cO6tKli6NMddLS0rRgwYIq4yMjI5vabAAA0MLOnDkjf3//Wss0KODMnTtXTz31VK1l9uzZo759+zakWpdLTU1VSkqK43VFRYVOnz6trl27ymKxNOuy7Ha7IiMjdfjwYU5/1YL1VDfWUf2wnuqH9VQ/rKf6cdd6MgxDZ86cqdclKQ0KOLNnz9akSZNqLRMVFdWQKh3CwsIkSQUFBQoPD3eMLygo0KBBgxxljh8/7jTfxYsXdfr0acf81bFarbJarU7j6ntnV2P5+fnx4agH1lPdWEf1w3qqH9ZT/bCe6scd66muIzeVGhRwgoODFRwc3KgG1aVnz54KCwtTZmamI9DY7XZt27bNcSdWXFycCgsLlZOTo5iYGEnS5s2bVVFRodjYWJe0CwAAtD0uu0380KFD2rVrlw4dOqTy8nLt2rVLu3btcnpmTd++fbVhwwZJksVi0cyZM/XEE09o48aN+vLLLzVx4kRFRERozJgxkqR+/fopKSlJycnJ2r59uz7++GPNmDFD48ePr/cdVAAAwPxcdpHxvHnztHr1asfrK6+8UpK0ZcsWjRw5UpKUm5vruKNJkh555BEVFxdr6tSpKiws1LBhw5Seni4fHx9HmTVr1mjGjBmKj4+Xh4eHxo4dq6VLl7qqGw1mtVo1f/78KqfE4Iz1VDfWUf2wnuqH9VQ/rKf6aQvryeXPwQEAAGhp/BYVAAAwHQIOAAAwHQIOAAAwHQIOAAAwHQIOAAAwHQJOM1q2bJl69OghHx8fxcbGavv27e5uUqvy+OOPy2KxOA2t7Wc93OHDDz/UzTffrIiICFksFr3xxhtO0w3D0Lx58xQeHq6OHTsqISFB+/btc09j3aiu9TRp0qQq21dSUpJ7GutGaWlpuuqqq3TJJZcoJCREY8aMUW5urlOZ8+fPa/r06eratas6d+6ssWPHqqCgwE0tbnn1WUcjR46ssj3dd999bmqxe/z5z3/WgAEDHE8rjouL03vvveeY3tq3IwJOM1m3bp1SUlI0f/587dy5UwMHDlRiYmKVn5Zo7376058qPz/fMXz00UfubpLbFRcXa+DAgVq2bFm1059++mktXbpUy5cv17Zt29SpUyclJibq/PnzLdxS96prPUlSUlKS0/b197//vQVb2Dps3bpV06dP16effqqMjAxduHBBo0aNUnFxsaPMrFmz9NZbb2n9+vXaunWrjh07pttvv92NrW5Z9VlHkpScnOy0PT399NNuarF7XHbZZXryySeVk5Ojzz77TNdff71uvfVWff3115LawHZkoFkMGTLEmD59uuN1eXm5ERERYaSlpbmxVa3L/PnzjYEDB7q7Ga2aJGPDhg2O1xUVFUZYWJjxzDPPOMYVFhYaVqvV+Pvf/+6GFrYO/72eDMMw7rnnHuPWW291S3tas+PHjxuSjK1btxqG8f324+XlZaxfv95RZs+ePYYkIzs7213NdKv/XkeGYRgjRowwfvOb37ivUa1UYGCg8de//rVNbEccwWkGZWVlysnJUUJCgmOch4eHEhISlJ2d7caWtT779u1TRESEoqKiNGHCBB06dMjdTWrV8vLyZLPZnLYtf39/xcbGsm1VIysrSyEhIerTp4+mTZumU6dOubtJblf5tPguXbpIknJycnThwgWnbapv377q1q1bu92m/nsdVVqzZo2CgoJ0xRVXKDU1VSUlJe5oXqtQXl6utWvXqri4WHFxcW1iO3LZTzW0JydPnlR5eblCQ0OdxoeGhmrv3r1ualXrExsbq1WrVqlPnz7Kz8/XggULdO211+qrr77SJZdc4u7mtUo2m02Sqt22Kqfhe0lJSbr99tvVs2dPHThwQL/97W81evRoZWdny9PT093Nc4uKigrNnDlT11xzja644gpJ329T3t7eCggIcCrbXrep6taRJP3yl79U9+7dFRERod27d2vOnDnKzc3V66+/7sbWtrwvv/xScXFxOn/+vDp37qwNGzYoOjpau3btavXbEQEHLWb06NGO/w8YMECxsbHq3r27/vGPf2jKlClubBnMYPz48Y7/9+/fXwMGDFCvXr2UlZWl+Ph4N7bMfaZPn66vvvqKa91qUdM6mjp1quP//fv3V3h4uOLj43XgwAH16tWrpZvpNn369NGuXbtUVFSk1157Tffcc4+2bt3q7mbVC6eomkFQUJA8PT2rXD1eUFCgsLAwN7Wq9QsICNBPfvIT7d+/391NabUqtx+2rYaLiopSUFBQu92+ZsyYobfffltbtmzRZZdd5hgfFhamsrIyFRYWOpVvj9tUTeuoOrGxsZLU7rYnb29v9e7dWzExMUpLS9PAgQP1pz/9qU1sRwScZuDt7a2YmBhlZmY6xlVUVCgzM1NxcXFubFnrdvbsWR04cEDh4eHubkqr1bNnT4WFhTltW3a7Xdu2bWPbqsORI0d06tSpdrd9GYahGTNmaMOGDdq8ebN69uzpND0mJkZeXl5O21Rubq4OHTrUbraputZRdXbt2iVJ7W57+m8VFRUqLS1tG9uRu69yNou1a9caVqvVWLVqlfHNN98YU6dONQICAgybzebuprUas2fPNrKysoy8vDzj448/NhISEoygoCDj+PHj7m6aW505c8b4/PPPjc8//9yQZCxevNj4/PPPjW+//dYwDMN48sknjYCAAOPNN980du/ebdx6661Gz549jXPnzrm55S2rtvV05swZ46GHHjKys7ONvLw844MPPjB+9rOfGZdffrlx/vx5dze9RU2bNs3w9/c3srKyjPz8fMdQUlLiKHPfffcZ3bp1MzZv3mx89tlnRlxcnBEXF+fGVresutbR/v37jYULFxqfffaZkZeXZ7z55ptGVFSUMXz4cDe3vGXNnTvX2Lp1q5GXl2fs3r3bmDt3rmGxWIxNmzYZhtH6tyMCTjN67rnnjG7duhne3t7GkCFDjE8//dTdTWpVxo0bZ4SHhxve3t7GpZdeaowbN87Yv3+/u5vldlu2bDEkVRnuuecewzC+v1X8scceM0JDQw2r1WrEx8cbubm57m20G9S2nkpKSoxRo0YZwcHBhpeXl9G9e3cjOTm5Xf6BUd06kmSsXLnSUebcuXPG/fffbwQGBhq+vr7GbbfdZuTn57uv0S2srnV06NAhY/jw4UaXLl0Mq9Vq9O7d23j44YeNoqIi9za8hf3qV78yunfvbnh7exvBwcFGfHy8I9wYRuvfjiyGYRgtd7wIAADA9bgGBwAAmA4BBwAAmA4BBwAAmA4BBwAAmA4BBwAAmA4BBwAAmA4BBwAAmA4BBwAAmA4BBwAAmA4BBwAAmA4BBwAAmM7/AyFpfUNHAnXhAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_acf(y, lags=30);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\Python311\\Lib\\site-packages\\statsmodels\\graphics\\tsaplots.py:348: FutureWarning: The default method 'yw' can produce PACF values outside of the [-1,1] interval. After 0.13, the default will change tounadjusted Yule-Walker ('ywm'). You can use this method now by setting method='ywm'.\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "image/png": 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7O1sjR47Utddeq6ysLM2aNUt33nmn3n//fXuZ9evXKykpSQsWLNCuXbvUv39/JSQknPcx5wAAoO1otruoLBaLNm7cqNGjR9dYZu7cuXr33XcdnjY6btw4FRQUKC0tTdIvv2fzhz/8Qc8//7ykX56OGhoaqnvvvVfz5s1z6joAAIDWoUU96C8jI0Px8fEO4xISEjRr1ixJUllZmTIzM5WcnGyf7ubmpvj4+CpP9Pyt0tJShx8trPw13q5du9br0eYAAMB1DMPQqVOnFBISct4Hb7aogJObm6vAwECHcYGBgbLZbDp9+rR+/vlnlZeXV1um8rdiqpOSkqKFCxc6pc0AAKB5HT58WBdddFGtZVpUwHGW5ORkJSUl2V8XFhbq4osv1uHDh+Xt7d3o+v9ny//Tqs8Pqryi6tk+dzeLJg0M0/1/vLTRywEAoC2z2WwKDQ3VBRdccN6yLSrgBAUFKS8vz2FcXl6evL291aFDB7m7u8vd3b3aMkFBQTXWa7VaHX6ZuZK3t3eTBJwJg3tr9Vd5cqvmaiaLRZo4uLe8vTs2ejkAAEB1urykRT0HJy4uTunp6Q7jtmzZori4OEmSh4eHoqOjHcpUVFQoPT3dXsYVwv066smb+8ntN9vb3WKRm0V68uZ+CvMj3AAA0JycegSnqKhI+/fvt7/Ozs5WVlaWunTpoosvvljJycn66aef9Morr0iS7r77bj3//POaM2eO7rjjDm3dulWvv/663n33XXsdSUlJmjhxogYMGKCYmBgtXbpUxcXFmjx5sjNX5bzGDAhVnwu9NfzZTyVJk68K059juxFuAABwAacGnK+++krXXnut/XXldTATJ07UqlWrlJOTo0OHDtmnh4eH691339X999+vZ599VhdddJFeeuklJSQk2MuMHTtWx44d0/z585Wbm6uoqCilpaVVufDYFbp1/TXMJP3xUnl5tKgzgAAAtBlt8tfEbTabfHx8VFhY2CTX4FQqKTunyPm/PJTwu0UJBBwAAJpQfT6/W9Q1OAAAAE2BgAMAAEyHgAMAAEyHgAMAAEyHgAMAAEyHgAMAAEyHgAMAAEyHgAMAAEyHgAMAAEyHgAMAAEyHgAMAAEyHgAMAAEyHgAMAAEyHgAMAAEyHgAMAAEyHgAMAAEyHgAMAAEyHgAMAAEyHgAMAAEyHgAMAAEyHgAMAAEyHgAMAAEyHgAMAAEyHgAMAAEyHgAMAAEyHgAMAAEyHgAMAAEyHgAMAAEyHgAMAAEyHgAMAAEyHgAMAAEyHgAMAAEyHgAMAAEyHgAMAAEyHgAMAAEynWQLOsmXLFBYWJk9PT8XGxmrnzp01lh0yZIgsFkuVYeTIkfYykyZNqjI9MTGxOVYFAAC0Au2cvYD169crKSlJqampio2N1dKlS5WQkKC9e/cqICCgSvk333xTZWVl9tcnTpxQ//79NWbMGIdyiYmJWrlypf211Wp13koAAIBWxelHcJYsWaKpU6dq8uTJioyMVGpqqry8vLRixYpqy3fp0kVBQUH2YcuWLfLy8qoScKxWq0O5zp07O3tVAABAK+HUgFNWVqbMzEzFx8f/ukA3N8XHxysjI6NOdbz88ssaN26cOnbs6DB+27ZtCggIUM+ePTV9+nSdOHGixjpKS0tls9kcBgAAYF5ODTjHjx9XeXm5AgMDHcYHBgYqNzf3vPPv3LlT33zzje68806H8YmJiXrllVeUnp6uJ598Utu3b9fw4cNVXl5ebT0pKSny8fGxD6GhoQ1fKQAA0OI5/Rqcxnj55ZfVt29fxcTEOIwfN26c/f99+/ZVv3791L17d23btk1Dhw6tUk9ycrKSkpLsr202GyEHAAATc+oRHD8/P7m7uysvL89hfF5enoKCgmqdt7i4WOvWrdOUKVPOu5yIiAj5+flp//791U63Wq3y9vZ2GAAAgHk5NeB4eHgoOjpa6enp9nEVFRVKT09XXFxcrfNu2LBBpaWl+vOf/3ze5Rw5ckQnTpxQcHBwo9sMAABaP6ffRZWUlKQXX3xRq1ev1p49ezR9+nQVFxdr8uTJkqQJEyYoOTm5ynwvv/yyRo8era5duzqMLyoq0oMPPqgvvvhCBw8eVHp6ukaNGqUePXooISHB2asDAABaAadfgzN27FgdO3ZM8+fPV25urqKiopSWlma/8PjQoUNyc3PMWXv37tWnn36qDz74oEp97u7u2r17t1avXq2CggKFhIRo2LBhWrx4Mc/CAQAAkiSLYRiGqxvR3Gw2m3x8fFRYWNik1+OUlJ1T5Pz3JUnfLUqQl0eLvoYbAIBWpT6f3/wWFQAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMJ1mCTjLli1TWFiYPD09FRsbq507d9ZYdtWqVbJYLA6Dp6enQxnDMDR//nwFBwerQ4cOio+P1759+5y9GgAAoJVwesBZv369kpKStGDBAu3atUv9+/dXQkKC8vPza5zH29tbOTk59uHHH390mP7UU0/pueeeU2pqqnbs2KGOHTsqISFBZ86ccfbqAACAVsDpAWfJkiWaOnWqJk+erMjISKWmpsrLy0srVqyocR6LxaKgoCD7EBgYaJ9mGIaWLl2qhx9+WKNGjVK/fv30yiuv6OjRo3rrrbecvToAAKAVcGrAKSsrU2ZmpuLj439doJub4uPjlZGRUeN8RUVF6tatm0JDQzVq1Ch9++239mnZ2dnKzc11qNPHx0exsbE11llaWiqbzeYwAAAA83JqwDl+/LjKy8sdjsBIUmBgoHJzc6udp2fPnlqxYoXefvttvfrqq6qoqNDAgQN15MgRSbLPV586U1JS5OPjYx9CQ0Mbu2oAAKAFa3F3UcXFxWnChAmKiorS4MGD9eabb8rf31///Oc/G1xncnKyCgsL7cPhw4ebsMUAAKClcWrA8fPzk7u7u/Ly8hzG5+XlKSgoqE51tG/fXpdffrn2798vSfb56lOn1WqVt7e3wwAAAMzLqQHHw8ND0dHRSk9Pt4+rqKhQenq64uLi6lRHeXm5/vvf/yo4OFiSFB4erqCgIIc6bTabduzYUec6AQCAubVz9gKSkpI0ceJEDRgwQDExMVq6dKmKi4s1efJkSdKECRN04YUXKiUlRZK0aNEiXXnllerRo4cKCgr09NNP68cff9Sdd94p6Zc7rGbNmqXHHntMl1xyicLDw/XII48oJCREo0ePdvbqAACAVsDpAWfs2LE6duyY5s+fr9zcXEVFRSktLc1+kfChQ4fk5vbrgaSff/5ZU6dOVW5urjp37qzo6Gh9/vnnioyMtJeZM2eOiouLNW3aNBUUFOiqq65SWlpalQcCAgCAtsliGIbh6kY0N5vNJh8fHxUWFjbp9TglZecUOf99SdJ3ixLk5eH0/AgAQJtRn8/vFncXFQAAQGMRcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOk0S8BZtmyZwsLC5OnpqdjYWO3cubPGsi+++KKuvvpqde7cWZ07d1Z8fHyV8pMmTZLFYnEYEhMTnb0aAACglXB6wFm/fr2SkpK0YMEC7dq1S/3791dCQoLy8/OrLb9t2zbddttt+uijj5SRkaHQ0FANGzZMP/30k0O5xMRE5eTk2IfXXnvN2asCAABaCacHnCVLlmjq1KmaPHmyIiMjlZqaKi8vL61YsaLa8mvWrNE999yjqKgo9erVSy+99JIqKiqUnp7uUM5qtSooKMg+dO7c2dmrAgAAWgmnBpyysjJlZmYqPj7+1wW6uSk+Pl4ZGRl1qqOkpERnz55Vly5dHMZv27ZNAQEB6tmzp6ZPn64TJ07UWEdpaalsNpvDAAAAzMupAef48eMqLy9XYGCgw/jAwEDl5ubWqY65c+cqJCTEISQlJibqlVdeUXp6up588klt375dw4cPV3l5ebV1pKSkyMfHxz6EhoY2fKUAAECL187VDajNE088oXXr1mnbtm3y9PS0jx83bpz9/3379lW/fv3UvXt3bdu2TUOHDq1ST3JyspKSkuyvbTYbIQcAABNz6hEcPz8/ubu7Ky8vz2F8Xl6egoKCap33mWee0RNPPKEPPvhA/fr1q7VsRESE/Pz8tH///mqnW61WeXt7OwwAAMC8nBpwPDw8FB0d7XCBcOUFw3FxcTXO99RTT2nx4sVKS0vTgAEDzrucI0eO6MSJEwoODm6SdgMAgNbN6XdRJSUl6cUXX9Tq1au1Z88eTZ8+XcXFxZo8ebIkacKECUpOTraXf/LJJ/XII49oxYoVCgsLU25urnJzc1VUVCRJKioq0oMPPqgvvvhCBw8eVHp6ukaNGqUePXooISHB2asDAABaAadfgzN27FgdO3ZM8+fPV25urqKiopSWlma/8PjQoUNyc/s1Z73wwgsqKyvTLbfc4lDPggUL9Oijj8rd3V27d+/W6tWrVVBQoJCQEA0bNkyLFy+W1Wp19uoAAIBWwGIYhuHqRjQ3m80mHx8fFRYWNun1OCVl5xQ5/31J0neLEuTl0aKv4QYAoFWpz+c3v0UFAABMh4ADAABMh4ADAABMh4ADAABMh4ADAABMh4ADAABMh4ADAABMh4ADAABMh4ADAABMh4ADAABMh4ADAABMh4ADAABMh4ADAABMh4ADAABMh4ADAABMh4ADAABMh4ADAABMh4ADAABMh4ADAABMh4ADAABMh4ADAABMh4ADAABMh4ADAABMh4ADAABMh4ADAABMh4ADAABMh4ADAABMh4ADAABMp52rG9DWZBw44eomAADgdHHdu7p0+QQcAGhGOYWntW3vMR0rKpV/J6uG9PRXsE8HVzcLMB0CDgA0k21787X8kx9kkWRIskjatPuo7romQoMvDXBx6+AqhF7nIOAAQDPIKTyt5Z/8IMP4JdxIv/77z49/UM9AbwX5eLqqeXARQq/zEHCAFohvdOazbe8x+4fY71kkfbQ3X7fFXNzMrWq52sJ7gNDrXAQcwIka8keab3TmdKyotNpwI/2yn48VlTZnc5pFQ0NKY94DrSkYEXqdi4CDZtea/gA1RkP+SLfVb3Su6BPNvUz/TtZaP8z8O1nPW0dreu80NKQ05j3gyi8HDdk3rTX0tpZ+SMBpw1zRSV31B6i517Whf6Tb4jc6V/QJVyxzSE9/bdp9tNpphqRre9a+3NZ0ZK9xIaVh7wFXfjlo6L5pitDb3FpTP2yWB/0tW7ZMYWFh8vT0VGxsrHbu3Flr+Q0bNqhXr17y9PRU37599d577zlMNwxD8+fPV3BwsDp06KD4+Hjt27fPmatgOtv25mv2hv9o8+6j+uKHE9q8+6hmb/iPtv+/fKct87d/gCoMOfz7z49/UG7hGacs1xXrWvlHujqVf6Sr0xTf6HIKT+u1nYf03NZ9em3nIeUUnq5Lk13CFX3CVf0w2KeD7romQpbfdAw3i2SxSHddE1Hrh6+r2ly57Pr2p4b2f6nh74HGLLMxGrNvhvT0r3Vdzxd6m5sr+2FDOP0Izvr165WUlKTU1FTFxsZq6dKlSkhI0N69exUQUHXnff7557rtttuUkpKi66+/XmvXrtXo0aO1a9cu9enTR5L01FNP6bnnntPq1asVHh6uRx55RAkJCfruu+/k6Vn3hF5Sdk7tys412bqW/KaukhrqPXO2vMmW11C5tjO1ftMJ69pRgd5N/03nwz15tX5b2bInV2OiQ5t0ma5a1zzbmVr/cOXZzlTbFzp7ta91G3X2al9rH/pk3zGt/PxglW9XdwwM11WX+NV3NZzOFX3CFcusFBveVSE+npr/zneSpD/2DtS1vQIU6O1Z6351VZsb2p8a2v+lhr8HGrPMxmjMvuns5aE7BoZrxWfZ9vndLL/UdcfAcPme5/0u/fI37pN9x3SiqExdO3no6kv8FVSHv2kNma++61rT52Bj1KdOi2EYNfWJJhEbG6s//OEPev755yVJFRUVCg0N1b333qt58+ZVKT927FgVFxdr8+bN9nFXXnmloqKilJqaKsMwFBISotmzZ+uBBx6QJBUWFiowMFCrVq3SuHHjqtRZWlqq0tJfU7/NZlNoaKhCZ70uN6tXU68yAABwgorSEh1eeqsKCwvl7e1da1mnnqIqKytTZmam4uPjf12gm5vi4+OVkZFR7TwZGRkO5SUpISHBXj47O1u5ubkOZXx8fBQbG1tjnSkpKfLx8bEPoaHO+XYGAABaBqeeojp+/LjKy8sVGBjoMD4wMFDff/99tfPk5uZWWz43N9c+vXJcTWV+Lzk5WUlJSfbXlUdwdv5/Q8+bAJvajh9OOrz+ZN8xrfzsYLWHJ+tySqH0bLnuXrNLkpQ6/gpZ27ufd54NmYeV9k2uKqo5dudmkRL7BJ33cHdDlptrO6OHNv5X1R0ztFiklJv6Vnu6qKHzSa5bV0n6dN9xrfg82+Hwfl33bZ7tjD7+zeHjay7xP++ptNTtB7Tz4Mkat1NMWBfdPbh7rXUcOlGsBZt+OX2SEBmoIb0CznvYujH7pzHzSs3bDxu73MZwxXZqbH9qTP+XGvYeaOwyXdWfGqKhf9sa8zexvusaG9GlzutTVzabTcFL61a2TdxFZbVaZbVWvRrdy6OdvDyadxN4/uYNk1N4Wis/P+hwPrOy0634PFt9LvSp11X/1vbuDvXXJL53oP79TfVh0JD0x95BdaqnvssN69pRd10ToX9+/EOVP0B3XROhbl07VjtfxoETtZ73/fzAiRrvLGqKdc21/Xrh3Du7jyq+d2Cd7sCKjwxUnwt99NHefPvdW9f2DKjTPu3WtaP+UsP2qEmgt2et2ynQ27PWda28O6LSlj15+mBP3nnvjmjM/mlon6jUkH3T2GX+Xl37f2M0ZZvr2t7G9qfG9H+pYe+Bxi6zJfSnuvq55Gyt1xz9XHK22v3T0Pmk+q+rMz5fz9WjTqd+uvv5+cnd3V15eXkO4/Py8hQUFFTtPEFBQbWWr/w3Ly9PwcHBDmWioqKasPXO56pbgivv5qipk9blj8Fv/xBsyDxc5w/9wZcGqGegd73+ADXmzqLGruvvP/TTvsnVv7/JrfMtkUE+ns12W3djbkP+7d0RlSrD9vlusW3snV8N6RNS4/ZNQ5fpSo1pc0Per429rV1q3v7f2GW2tv7U0FvMG3tremt67zg14Hh4eCg6Olrp6ekaPXq0pF8uMk5PT9fMmTOrnScuLk7p6emaNWuWfdyWLVsUFxcnSQoPD1dQUJDS09PtgcZms2nHjh2aPn26M1enybnyIU+N6aTN/aHvqjdkYz70XaExYa4xYbspnuVR3z7RFPvGFR++jdWQNjf0/doUX4Rai9bYnxoaQFtrcG0Ip5+fSUpK0sSJEzVgwADFxMRo6dKlKi4u1uTJkyVJEyZM0IUXXqiUlBRJ0l//+lcNHjxYf//73zVy5EitW7dOX331lZYvXy5JslgsmjVrlh577DFdcskl9tvEQ0JC7CGqtXD1Q54a0kld8aHvqjdka3zoXkPDXGPCdlPsn/pqjfvGFRr7fm1N39YbozX2p4YG0LYUXJ0ecMaOHatjx45p/vz5ys3NVVRUlNLS0uwXCR86dEhubr/ezDVw4ECtXbtWDz/8sB566CFdcskleuutt+zPwJGkOXPmqLi4WNOmTVNBQYGuuuoqpaWl1esZOC1BU3wwNPRUUUO54g+Bq96QrfUx6g0Jc40J267YP6113zS3pni/tpZv643RWvtTQwNoWwmuzXKF7cyZM2s8JbVt27Yq48aMGaMxY8bUWJ/FYtGiRYu0aNGipmqiS7j6+pCGcNUfgtZ0jrs1amzYbu794+p909xfLBqqtX5wNzdX96fGaGgAbQvBtU3cRdWStbbrQ1z5h6C1nONujZriKExruaC6sVzxxaKhWvMHd3NqS+/1tqRZfosKtav8YLjvukt0W8zFdbzQ1zW/u9LafjulMX7720GVvxlU198Oao0GXxqgJWOidH2/EF0Z0VXX9wvRkjFRLe5DW3Ldvqnpi0VL/S2etvR+bYy29l5vKziC00q56tBzW7pATWo756ortabD1q7YN63tYtS29n5tjLb2Xm8LCDitlCsPPbe1PwSt6UO/rWnufdMar2lpa+/XxuC9bi4EnGYW171rk9QT5OOpzTWcM5akpD9eqjA/5zxBs9JNV1zo1PqBlubjfce0M/ukyqt5Vr2bxaKoUN8me483Nd6vaGu4BqeVCvfrqCdv7ic3i+TuZnH498mb+zk93ABt0a0DQmVU90M8kgzD0NgB/JAv0FJwBKcVGzMgVH8I66L1Xx3WkZ9P66LOHTR2QCjhBnCSyi8Wc/+1WxaLRYZh2P/liwXQsliMmr6OmJjNZpOPj48KCwub/dfEAbR+B48X88UCcIH6fH5zBAcA6inMr6PmJvZydTMA1IJrcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOk4NeCcPHlS48ePl7e3t3x9fTVlyhQVFRXVWv7ee+9Vz5491aFDB1188cW67777VFhY6FDOYrFUGdatW+fMVQEAAK1IO2dWPn78eOXk5GjLli06e/asJk+erGnTpmnt2rXVlj969KiOHj2qZ555RpGRkfrxxx9199136+jRo3rjjTccyq5cuVKJiYn2176+vs5cFQAA0IpYDMMwnFHxnj17FBkZqS+//FIDBgyQJKWlpWnEiBE6cuSIQkJC6lTPhg0b9Oc//1nFxcVq1+6XPGaxWLRx40aNHj26QW2z2Wzy8fFRYWGhvL29G1QHAABoXvX5/HbaKaqMjAz5+vraw40kxcfHy83NTTt27KhzPZUrURluKs2YMUN+fn6KiYnRihUrVFtOKy0tlc1mcxgAAIB5Oe0UVW5urgICAhwX1q6dunTpotzc3DrVcfz4cS1evFjTpk1zGL9o0SJdd9118vLy0gcffKB77rlHRUVFuu+++6qtJyUlRQsXLmzYigAAgFan3kdw5s2bV+1Fvr8dvv/++0Y3zGazaeTIkYqMjNSjjz7qMO2RRx7RoEGDdPnll2vu3LmaM2eOnn766RrrSk5OVmFhoX04fPhwo9sHAABarnofwZk9e7YmTZpUa5mIiAgFBQUpPz/fYfy5c+d08uRJBQUF1Tr/qVOnlJiYqAsuuEAbN25U+/btay0fGxurxYsXq7S0VFartcp0q9Va7XgAAGBO9Q44/v7+8vf3P2+5uLg4FRQUKDMzU9HR0ZKkrVu3qqKiQrGxsTXOZ7PZlJCQIKvVqnfeeUeenp7nXVZWVpY6d+5MiAEAAJKceA1O7969lZiYqKlTpyo1NVVnz57VzJkzNW7cOPsdVD/99JOGDh2qV155RTExMbLZbBo2bJhKSkr06quvOlwQ7O/vL3d3d23atEl5eXm68sor5enpqS1btujxxx/XAw884KxVAQAArYxTn4OzZs0azZw5U0OHDpWbm5tuvvlmPffcc/bpZ8+e1d69e1VSUiJJ2rVrl/0Oqx49ejjUlZ2drbCwMLVv317Lli3T/fffL8Mw1KNHDy1ZskRTp0515qoAAIBWxGnPwWnJeA4OAACtT4t4Dg4AAICrEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpODXgnDx5UuPHj5e3t7d8fX01ZcoUFRUV1TrPkCFDZLFYHIa7777bocyhQ4c0cuRIeXl5KSAgQA8++KDOnTvnzFUBAACtSDtnVj5+/Hjl5ORoy5YtOnv2rCZPnqxp06Zp7dq1tc43depULVq0yP7ay8vL/v/y8nKNHDlSQUFB+vzzz5WTk6MJEyaoffv2evzxx522LgAAoPWwGIZhOKPiPXv2KDIyUl9++aUGDBggSUpLS9OIESN05MgRhYSEVDvfkCFDFBUVpaVLl1Y7/d///reuv/56HT16VIGBgZKk1NRUzZ07V8eOHZOHh8d522az2eTj46PCwkJ5e3s3bAUBAECzqs/nt9NOUWVkZMjX19cebiQpPj5ebm5u2rFjR63zrlmzRn5+furTp4+Sk5NVUlLiUG/fvn3t4UaSEhISZLPZ9O2331ZbX2lpqWw2m8MAAADMy2mnqHJzcxUQEOC4sHbt1KVLF+Xm5tY43+23365u3bopJCREu3fv1ty5c7V37169+eab9np/G24k2V/XVG9KSooWLlzYmNUBAACtSL0Dzrx58/Tkk0/WWmbPnj0NbtC0adPs/+/bt6+Cg4M1dOhQHThwQN27d29QncnJyUpKSrK/ttlsCg0NbXAbAQBAy1bvgDN79mxNmjSp1jIREREKCgpSfn6+w/hz587p5MmTCgoKqvPyYmNjJUn79+9X9+7dFRQUpJ07dzqUycvLk6Qa67VarbJarXVeJgAAaN3qHXD8/f3l7+9/3nJxcXEqKChQZmamoqOjJUlbt25VRUWFPbTURVZWliQpODjYXu/f/vY35efn20+BbdmyRd7e3oqMjKzn2gAAADNy2kXGvXv3VmJioqZOnaqdO3fqs88+08yZMzVu3Dj7HVQ//fSTevXqZT8ic+DAAS1evFiZmZk6ePCg3nnnHU2YMEHXXHON+vXrJ0kaNmyYIiMj9Ze//EX/+c9/9P777+vhhx/WjBkzOEoDAAAkOflBf2vWrFGvXr00dOhQjRgxQldddZWWL19un3727Fnt3bvXfpeUh4eHPvzwQw0bNky9evXS7NmzdfPNN2vTpk32edzd3bV582a5u7srLi5Of/7znzVhwgSH5+YAAIC2zWnPwWnJeA4OAACtT4t4Dg4AAICrEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpODXgnDx5UuPHj5e3t7d8fX01ZcoUFRUV1Vj+4MGDslgs1Q4bNmywl6tu+rp165y5KgAAoBVp58zKx48fr5ycHG3ZskVnz57V5MmTNW3aNK1du7ba8qGhocrJyXEYt3z5cj399NMaPny4w/iVK1cqMTHR/trX17fJ2w8AAFonpwWcPXv2KC0tTV9++aUGDBggSfrHP/6hESNG6JlnnlFISEiVedzd3RUUFOQwbuPGjbr11lvVqVMnh/G+vr5VygIAAEhOPEWVkZEhX19fe7iRpPj4eLm5uWnHjh11qiMzM1NZWVmaMmVKlWkzZsyQn5+fYmJitGLFChmGUWM9paWlstlsDgMAADAvpx3Byc3NVUBAgOPC2rVTly5dlJubW6c6Xn75ZfXu3VsDBw50GL9o0SJdd9118vLy0gcffKB77rlHRUVFuu+++6qtJyUlRQsXLmzYigAAgFan3kdw5s2bV+OFwJXD999/3+iGnT59WmvXrq326M0jjzyiQYMG6fLLL9fcuXM1Z84cPf300zXWlZycrMLCQvtw+PDhRrcPAAC0XPU+gjN79mxNmjSp1jIREREKCgpSfn6+w/hz587p5MmTdbp25o033lBJSYkmTJhw3rKxsbFavHixSktLZbVaq0y3Wq3VjgcAAOZU74Dj7+8vf3//85aLi4tTQUGBMjMzFR0dLUnaunWrKioqFBsbe975X375Zd144411WlZWVpY6d+5MiAEAAJKceA1O7969lZiYqKlTpyo1NVVnz57VzJkzNW7cOPsdVD/99JOGDh2qV155RTExMfZ59+/fr48//ljvvfdelXo3bdqkvLw8XXnllfL09NSWLVv0+OOP64EHHnDWqgAAgFbGqc/BWbNmjWbOnKmhQ4fKzc1NN998s5577jn79LNnz2rv3r0qKSlxmG/FihW66KKLNGzYsCp1tm/fXsuWLdP9998vwzDUo0cPLVmyRFOnTnXmqgAAgFbEYtR2f7VJ2Ww2+fj4qLCwUN7e3q5uDgAAqIP6fH7zW1QAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0nBZw/va3v2ngwIHy8vKSr69vneYxDEPz589XcHCwOnTooPj4eO3bt8+hzMmTJzV+/Hh5e3vL19dXU6ZMUVFRkRPWAAAAtFZOCzhlZWUaM2aMpk+fXud5nnrqKT333HNKTU3Vjh071LFjRyUkJOjMmTP2MuPHj9e3336rLVu2aPPmzfr44481bdo0Z6wCAABopSyGYRjOXMCqVas0a9YsFRQU1FrOMAyFhIRo9uzZeuCBByRJhYWFCgwM1KpVqzRu3Djt2bNHkZGR+vLLLzVgwABJUlpamkaMGKEjR44oJCSkTm2y2Wzy8fFRYWGhvL29G7V+AACgedTn87tdM7XpvLKzs5Wbm6v4+Hj7OB8fH8XGxiojI0Pjxo1TRkaGfH197eFGkuLj4+Xm5qYdO3bopptuqrbu0tJSlZaW2l8XFhZK+mVDAQCA1qHyc7sux2ZaTMDJzc2VJAUGBjqMDwwMtE/Lzc1VQECAw/R27dqpS5cu9jLVSUlJ0cKFC6uMDw0NbWyzAQBAMzt16pR8fHxqLVOvgDNv3jw9+eSTtZbZs2ePevXqVZ9qnS45OVlJSUn21xUVFTp58qS6du0qi8XSpMuy2WwKDQ3V4cOHOf1VC7bT+bGN6obtVDdsp7phO9WNq7aTYRg6depUnS5JqVfAmT17tiZNmlRrmYiIiPpUaRcUFCRJysvLU3BwsH18Xl6eoqKi7GXy8/Md5jt37pxOnjxpn786VqtVVqvVYVxd7+xqKG9vb94cdcB2Oj+2Ud2wneqG7VQ3bKe6ccV2Ot+Rm0r1Cjj+/v7y9/dvUIPOJzw8XEFBQUpPT7cHGpvNph07dtjvxIqLi1NBQYEyMzMVHR0tSdq6dasqKioUGxvrlHYBAIDWx2m3iR86dEhZWVk6dOiQysvLlZWVpaysLIdn1vTq1UsbN26UJFksFs2aNUuPPfaY3nnnHf33v//VhAkTFBISotGjR0uSevfurcTERE2dOlU7d+7UZ599ppkzZ2rcuHF1voMKAACYn9MuMp4/f75Wr15tf3355ZdLkj766CMNGTJEkrR37177HU2SNGfOHBUXF2vatGkqKCjQVVddpbS0NHl6etrLrFmzRjNnztTQoUPl5uamm2++Wc8995yzVqPerFarFixYUOWUGByxnc6PbVQ3bKe6YTvVDdupblrDdnL6c3AAAACaG79FBQAATIeAAwAATIeAAwAATIeAAwAATIeAAwAATIeA04SWLVumsLAweXp6KjY2Vjt37nR1k1qURx99VBaLxWFoaT/r4Qoff/yxbrjhBoWEhMhiseitt95ymG4YhubPn6/g4GB16NBB8fHx2rdvn2sa60Ln206TJk2q0r8SExNd01gXSklJ0R/+8AddcMEFCggI0OjRo7V3716HMmfOnNGMGTPUtWtXderUSTfffLPy8vJc1OLmV5dtNGTIkCr96e6773ZRi13jhRdeUL9+/exPK46Li9O///1v+/SW3o8IOE1k/fr1SkpK0oIFC7Rr1y71799fCQkJVX5aoq277LLLlJOTYx8+/fRTVzfJ5YqLi9W/f38tW7as2ulPPfWUnnvuOaWmpmrHjh3q2LGjEhISdObMmWZuqWudbztJUmJiokP/eu2115qxhS3D9u3bNWPGDH3xxRfasmWLzp49q2HDhqm4uNhe5v7779emTZu0YcMGbd++XUePHtWf/vQnF7a6edVlG0nS1KlTHfrTU0895aIWu8ZFF12kJ554QpmZmfrqq6903XXXadSoUfr2228ltYJ+ZKBJxMTEGDNmzLC/Li8vN0JCQoyUlBQXtqplWbBggdG/f39XN6NFk2Rs3LjR/rqiosIICgoynn76afu4goICw2q1Gq+99poLWtgy/H47GYZhTJw40Rg1apRL2tOS5efnG5KM7du3G4bxS/9p3769sWHDBnuZPXv2GJKMjIwMVzXTpX6/jQzDMAYPHmz89a9/dV2jWqjOnTsbL730UqvoRxzBaQJlZWXKzMxUfHy8fZybm5vi4+OVkZHhwpa1PPv27VNISIgiIiI0fvx4HTp0yNVNatGys7OVm5vr0Ld8fHwUGxtL36rGtm3bFBAQoJ49e2r69Ok6ceKEq5vkcpVPi+/SpYskKTMzU2fPnnXoU7169dLFF1/cZvvU77dRpTVr1sjPz099+vRRcnKySkpKXNG8FqG8vFzr1q1TcXGx4uLiWkU/ctpPNbQlx48fV3l5uQIDAx3GBwYG6vvvv3dRq1qe2NhYrVq1Sj179lROTo4WLlyoq6++Wt98840uuOACVzevRcrNzZWkavtW5TT8IjExUX/6058UHh6uAwcO6KGHHtLw4cOVkZEhd3d3VzfPJSoqKjRr1iwNGjRIffr0kfRLn/Lw8JCvr69D2bbap6rbRpJ0++23q1u3bgoJCdHu3bs1d+5c7d27V2+++aYLW9v8/vvf/youLk5nzpxRp06dtHHjRkVGRiorK6vF9yMCDprN8OHD7f/v16+fYmNj1a1bN73++uuaMmWKC1sGMxg3bpz9/3379lW/fv3UvXt3bdu2TUOHDnVhy1xnxowZ+uabb7jWrRY1baNp06bZ/9+3b18FBwdr6NChOnDggLp3797czXSZnj17KisrS4WFhXrjjTc0ceJEbd++3dXNqhNOUTUBPz8/ubu7V7l6PC8vT0FBQS5qVcvn6+urSy+9VPv373d1U1qsyv5D36q/iIgI+fn5tdn+NXPmTG3evFkfffSRLrroIvv4oKAglZWVqaCgwKF8W+xTNW2j6sTGxkpSm+tPHh4e6tGjh6Kjo5WSkqL+/fvr2WefbRX9iIDTBDw8PBQdHa309HT7uIqKCqWnpysuLs6FLWvZioqKdODAAQUHB7u6KS1WeHi4goKCHPqWzWbTjh076FvnceTIEZ04caLN9S/DMDRz5kxt3LhRW7duVXh4uMP06OhotW/f3qFP7d27V4cOHWozfep826g6WVlZktTm+tPvVVRUqLS0tHX0I1df5WwW69atM6xWq7Fq1Srju+++M6ZNm2b4+voaubm5rm5aizF79mxj27ZtRnZ2tvHZZ58Z8fHxhp+fn5Gfn+/qprnUqVOnjK+//tr4+uuvDUnGkiVLjK+//tr48ccfDcMwjCeeeMLw9fU13n77bWP37t3GqFGjjPDwcOP06dMubnnzqm07nTp1ynjggQeMjIwMIzs72/jwww+NK664wrjkkkuMM2fOuLrpzWr69OmGj4+PsW3bNiMnJ8c+lJSU2MvcfffdxsUXX2xs3brV+Oqrr4y4uDgjLi7Oha1uXufbRvv37zcWLVpkfPXVV0Z2drbx9ttvGxEREcY111zj4pY3r3nz5hnbt283srOzjd27dxvz5s0zLBaL8cEHHxiG0fL7EQGnCf3jH/8wLr74YsPDw8OIiYkxvvjiC1c3qUUZO3asERwcbHh4eBgXXnihMXbsWGP//v2ubpbLffTRR4akKsPEiRMNw/jlVvFHHnnECAwMNKxWqzF06FBj7969rm20C9S2nUpKSoxhw4YZ/v7+Rvv27Y1u3boZU6dObZNfMKrbRpKMlStX2sucPn3auOeee4zOnTsbXl5exk033WTk5OS4rtHN7Hzb6NChQ8Y111xjdOnSxbBarUaPHj2MBx980CgsLHRtw5vZHXfcYXTr1s3w8PAw/P39jaFDh9rDjWG0/H5kMQzDaL7jRQAAAM7HNTgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0CDgAAMB0/n848KObPYo3ggAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_pacf(y, lags=30);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice there isn't really much by the way of autocorrelation in y - it looks like white noise. This mimics the residuals *after* fitting a good model to the original data.\n",
    "\n",
    "However, you might still suspect a problem with a variance dependent on time. To test this, first we test the same correlation, but on the squared residuals:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_acf(y**2, lags=30);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_pacf(y**2, lags=30);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here you see a strong lagged autocorrelation at lag 1. If you see this result (for any reasonable lag), it is time to fit an ARCH model.\n",
    "\n",
    "There is a useful arch model in the `arch` package"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "from arch import arch_model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = arch_model(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration:      1,   Func. Count:      6,   Neg. LLF: 324290.29566441604\n",
      "Iteration:      2,   Func. Count:     12,   Neg. LLF: 226075.52410248906\n",
      "Iteration:      3,   Func. Count:     19,   Neg. LLF: 6830.113526740106\n",
      "Iteration:      4,   Func. Count:     25,   Neg. LLF: 3030.8231653584726\n",
      "Iteration:      5,   Func. Count:     31,   Neg. LLF: 2563.815598056422\n",
      "Iteration:      6,   Func. Count:     36,   Neg. LLF: 2560.0897150451437\n",
      "Iteration:      7,   Func. Count:     41,   Neg. LLF: 2558.689580480894\n",
      "Iteration:      8,   Func. Count:     46,   Neg. LLF: 2558.685772194439\n",
      "Iteration:      9,   Func. Count:     51,   Neg. LLF: 2558.6852215224003\n",
      "Iteration:     10,   Func. Count:     56,   Neg. LLF: 2558.685118276649\n",
      "Iteration:     11,   Func. Count:     60,   Neg. LLF: 2558.6851193875236\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2558.685118276649\n",
      "            Iterations: 11\n",
      "            Function evaluations: 60\n",
      "            Gradient evaluations: 11\n"
     ]
    }
   ],
   "source": [
    "results = model.fit()  # As per statsmodels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Constant Mean - GARCH Model Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>          <td>y</td>         <th>  R-squared:         </th>  <td>   0.000</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Mean Model:</th>       <td>Constant Mean</td>   <th>  Adj. R-squared:    </th>  <td>   0.000</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Vol Model:</th>            <td>GARCH</td>       <th>  Log-Likelihood:    </th> <td>  -2558.69</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Distribution:</th>        <td>Normal</td>       <th>  AIC:               </th> <td>   5125.37</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>        <td>Maximum Likelihood</td> <th>  BIC:               </th> <td>   5145.00</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                        <td></td>          <th>  No. Observations:  </th>    <td>1000</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>           <td>Fri, Feb 09 2024</td>  <th>  Df Residuals:      </th>     <td>999</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>               <td>01:02:28</td>      <th>  Df Model:          </th>      <td>1</td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Mean Model</caption>\n",
       "<tr>\n",
       "   <td></td>     <th>coef</th>     <th>std err</th>      <th>t</th>       <th>P>|t|</th>   <th>95.0% Conf. Int.</th> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>mu</th> <td>    0.0162</td> <td>7.743e-02</td> <td>    0.210</td> <td>    0.834</td> <td>[ -0.136,  0.168]</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Volatility Model</caption>\n",
       "<tr>\n",
       "      <td></td>        <th>coef</th>     <th>std err</th>      <th>t</th>       <th>P>|t|</th>   <th>95.0% Conf. Int.</th> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>omega</th>    <td>    5.0192</td> <td>    1.077</td> <td>    4.662</td> <td>3.138e-06</td> <td>[  2.909,  7.129]</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>alpha[1]</th> <td>    0.6676</td> <td>    0.111</td> <td>    6.040</td> <td>1.536e-09</td> <td>[  0.451,  0.884]</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>beta[1]</th>  <td>2.6513e-13</td> <td>    0.145</td> <td>1.829e-12</td> <td>    1.000</td> <td>[ -0.284,  0.284]</td>\n",
       "</tr>\n",
       "</table><br/><br/>Covariance estimator: robust"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                     Constant Mean - GARCH Model Results                      \n",
       "==============================================================================\n",
       "Dep. Variable:                      y   R-squared:                       0.000\n",
       "Mean Model:             Constant Mean   Adj. R-squared:                  0.000\n",
       "Vol Model:                      GARCH   Log-Likelihood:               -2558.69\n",
       "Distribution:                  Normal   AIC:                           5125.37\n",
       "Method:            Maximum Likelihood   BIC:                           5145.00\n",
       "                                        No. Observations:                 1000\n",
       "Date:                Fri, Feb 09 2024   Df Residuals:                      999\n",
       "Time:                        01:02:28   Df Model:                            1\n",
       "                               Mean Model                               \n",
       "========================================================================\n",
       "                 coef    std err          t      P>|t|  95.0% Conf. Int.\n",
       "------------------------------------------------------------------------\n",
       "mu             0.0162  7.743e-02      0.210      0.834 [ -0.136,  0.168]\n",
       "                            Volatility Model                            \n",
       "========================================================================\n",
       "                 coef    std err          t      P>|t|  95.0% Conf. Int.\n",
       "------------------------------------------------------------------------\n",
       "omega          5.0192      1.077      4.662  3.138e-06 [  2.909,  7.129]\n",
       "alpha[1]       0.6676      0.111      6.040  1.536e-09 [  0.451,  0.884]\n",
       "beta[1]    2.6513e-13      0.145  1.829e-12      1.000 [ -0.284,  0.284]\n",
       "========================================================================\n",
       "\n",
       "Covariance estimator: robust\n",
       "\"\"\""
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can then use the ARCH model to predict the next values, by taking the fitted model and asking it to forecast into the future. This is the predicted variance of the next value in the series."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.01623977645451202"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Get the last prediction when forcasting into the future. \n",
    "# This weird function call just gets us the \"next\" prediction.\n",
    "# The actual forecast result has lots more information\n",
    "prediction = results.forecast(horizon=1, start=None).mean.iloc[-1]['h.1']\n",
    "prediction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From here, you can see the values for alpha are non-zero, based on the p test and beta are approximately zero. Further, there is the omega value that is 5.0192 (we used 5 for generating the data) above.\n",
    "\n",
    "#### Exercise\n",
    "\n",
    "1. Map the coefficients in the volatility results summary above to the model for GARCH above. Check the documentation for the function if needed.\n",
    "2. Modify the code we used to *create* the data, adding a second lag term. Fit the GARCH(1,1) model again, and see what the results look like when the model does not have enough specificity. Then fit a GARCH(2,2) model and observe the improvement."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Extended exercise Combining the steps\n",
    "\n",
    "We'll now combine the steps we have covered, specifically ARIMA and GARCH, to fit a model to predict the price of the market. While this is an exercise here, a template for this code, with some parts missing, is available at:\n",
    "\n",
    "`solutions/arima_garch_prediction_template.py`\n",
    "\n",
    "If you get stuck, feel free to start with this template and fill out the details. If you are more confident, try solving the exercise without it.\n",
    "\n",
    "The general process for using ARIMA and GARCH together for forecasting is to:\n",
    "\n",
    "1. Download data, such as from Quandl, for the asset you are predicting\n",
    "1. Compute the log returns for each day\n",
    "1. For each day in your dataset:\n",
    "    1. Fit multiple ARIMA models on the data *up to that day* and choose the best one (or use an automatic choice)\n",
    "    1. Fit a GARCH model to the residuals of the ARIMA model\n",
    "    1. Use the fitted GARCH model to predict the next step\n",
    "    1. If positive, buy. If negative, sell\n",
    "3. Backtest strategy and compare against the market gain over that time (i.e. just buying and holding)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "More information: https://arch.readthedocs.io/en/latest/univariate/introduction.html"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*For solutions, see `solutions/arch_models.py`*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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